### Doing the Math, How to Reinvest Your Gains

Landlord Schmandlord wrote a blog post on the 1st about whether it is better to pay off an existing mortgage with your profits, or reinvest in a new home. He makes some solid claims in there about getting higher returns and greater tax advantages by reinvesting your profits into a new property, and then ends his post with a call to "What do you guys think?" I've never been the short to back down from a challenge, so being a very techincal sort of person, I decided to go ahead and model his two scenarios and do the math to see which plan is better and by how much. And as I sat down and considered how I'd approach this, I realized that it's a great opportunity to share with you how I go about making models. Using only Excel and an internet connection, I'm going to walk you through how I go about trying to answer questions like these.

To be honest, I'm a bit of a geek and modelling is one of the more fun aspects of investing (at least for me). Questions like this are what I invest for. Afterall, it's extremely applicable (should I work on only one house at a time?) but the answer isn't immeaditely clear. For those of us that are less mathematically inclined, I'll try to give good layman explinations of everything I do, and what each figure means. My goal is for you to walk away after reading this and feel like you have a good understanding of how to approach a similar problem in the future (maybe when looking at buying a new investment property later on).

We're going to compare two scenarios, Jim and Pablo. Jim is going to buy a house and use all the profits from that house to pay off the mortgage. Once his mortgage is paid off, he'll save up for another down payment and do the same thing with a second house. Pablo, on the other hand, will save his profits from his first house until he has enough to make a down payment on a second. He'll then buy his second and save for his third. His mortgages will be paid strictly according to schedule. We'll project their networths 20 years from the start date and see who made it out on top.

The first thing we need to talk about are assumptions. There are many variables involved in real estate, things that we don't have a solid answer to until they actually happen (what will Jim's mortgage rate be? How much will it cost Pablo to fix a leaky roof? 10 years from now, what will rents be?). Since we can't claim to know the answers to these questions, we'll just build estimates into our model. Some of our assumptions will be as follows (with the important figures highlighted in red):

- Our mortgages will all be secured at 6.65%. According to Freddie Mac, the average mortgage secured last week was 6.14%. But we don't want to pay points (the average borrower paid 0.4) and a non-owner-occupied property usually gets a slightly higher rate.
- Our first house (for each) will be bought at $235,000. The median home price for Q3 in the US was $232,300.
- Our rents will start out at $1,500 per month. As I wrote in an earlier post about pricing, a common goal is to get rent to equal 1% of the value of the property, but that typically isn't possible with single family homes.
- The value of the homes will increase by an average of 3% a year over the next 20 years. Yes this is probably on the conservative side, but not by too much. Traditionally real estate appreciates at a pace just ahead of inflation, and we are coming down from one of the biggest bubbles of all-time.
- Rents will increase by 3% a year as well. For obvious reasons, rents go up when prices go up, and can come back down when prices come down.
- Annual taxes, insurance and association fees will equal 0.5% of the current value of the home (taxes will go up, even with a fixed rate mortgage).
- Jim and Pablo will only buy a house when they think it can produce a positive cashflow. Under our model that will mean a down payment of 10%.
- Jim and Pablo will each start out with 1 house, 20% down. The reason they start with 20% down is to help speed up the model and exaggerate the differences between the two, and do so while making very realistic starting conditions.

But I'd like to take a second to talk about assumptions. Most everyone has heard that good old saying, "Assumptions make an ASS out of U and ME" (if you don't get it, just write the bolded letter down on a piece of paper).

Anyone who has every done mathematical proofs in college can attest to the fact that assumptions are everything. Many a mathematician has been told "your proof is untouchable... but I disgree with your assumptions." For example, I can mathematical prove the number of angel that can dance on the head of a pin, if I make an assumption about the size of an angel. The math I do may be perfect, but if the assumption is wrong all my work is for naught.

Maybe a more hard hitting example might be that infamous flipper Casey Serin. His business model (whether he realizes it or not) was validated in his head by the assumption that real estate prices would continue to climb. When that assumption failed, his entire "business" came crashing down around him, now he's on the hook for over $2 million. In fact you can take any business model and validate it or destroy it simply by changing the assumptions.

Assumptions are pretty scary stuff, they can destroy a business. So where are we supposed to get assumptions from? Well, like most "expert opinions", assumptions are simply guesses. Will real estate return an annualized 3% over the next 20 years? No one will know that until 2026.

So when choosing your assumptions, consider two things carefully.

What is the historical average? Housing has historically increased at a rate just over inflation. Unless you have some solid evidence that suggests that the historical trend will change, stay close to the trend.

Be pessimistic. In most things I want people to be optomistic. I'm a huge fan of the theory of self-fulfilling prophecies, that the act of believing something greatly increases it's chances of occuring. For example a student who honestly believes he's going to fail a class is always going to underperform an equal student who think he could do well (if you hadn't noticed the connection yet, the picture at the top is of Oedipus, a very famous self-fulfilling prophecy). But while I think that every entreprenuer needs to be hopelessly optomistic about their ventures, when making models I propose the opposite. Because if your model can withstand the worst conditions you forsee, then when things actually go well you'll be in fantastic shape.

Currently, in most of my models, I assume a annualized 3% appreciation from real estate over the next 15 years or so, which I believe is a fairly conservative estimate (depending on your area. Vegas and Phoenix might be lucky to average a annualized 3% return over 15 years). Over a shorter timeline, I'm much more pessimistic. Since the area I own in didn't over-inflate as much as the major cities, I tend to look at near 0% appreciation for the next 3-4 years (as a worst case scenario).

I'll continue this tomorrow when we go about setting up Excel to try to model Jim's busines

Updated: I just reached a major milestone. This was the first post I've written that contained no misspellings! Spellcheck just gave me the big thumb's up!

## 6 comments:

Sorry to rain on your parade, but your spell checker must have missed "optomistic". :)

Love the blog, keep up the good work! I look forward to the conclusion of this article.

Great article. Glad to see someone blogging who is trained in the rigors of mathematics.

Question: where are you getting your numbers on the long-term appreciation rates of real-estate and its relationship to inflation?

Steve - Thanks for ruining my day. I'm a programmer, I should know better than to trust technology.

Joe - I ran some calculations based on the Census Bureau's numbers. You can see the figures I was working with here:

http://www.census.gov/hhes/www/housing/census/historic/values.html

I'll make a note of it in my next post, but from 1960 to 200 housing returned an annualized 1.8% over inflation. From 1950 to 2000 was 1.99% and from 1970 to 2000 was 2.04%.

According to the latest numbers from the Bureau of Labor Statistics inflation over the last decade has averaged out to about 2.5% a year.

ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt

Maybe 3% is overly pessimistic as an annualized rate of gain for the next 20 years. Now this will have an impact on our model, since Jim will essentially be earning 6.65% on his money (by paying off his loan quickly... minus taxes), so we'll have to play with some numbers at the end and see how it affects our model.

I think that you can not leave out return on investment in this. I can see no way paying off one house before buying another will ever reach anywhere close to the other. Unless you put a value on the security you gain buy paying one off. Just my 2cents and thats exactly what its worth. Cant wait to see the results.

explinations was mispelt also

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